Closed Time-Domain Solutions for 1D Scattering and Inverse Scattering in Anisotropic Medium

A time-domain closed-form approximation is presented for the scattering and inverse problem of one dimensional (ID) inhomogeneous anisotropic medium in the gyrotropic media. The Maxwell equations in tensor form are transformed into two independent scalar wave equations by using the half-power matrix and eigenvalue decomposition in frequency domain. Then the time-domain solutions can be obtained by using first-order Wentzel-Kramers-Brillouin (WKB) solution and inverse Fourier transform. Numerical examples for direct and inverse problem are given to validate the proposed solutions. We show that the proposed formulation for inverse scattering works surprisingly well even for the cases of high contrast and steep slopes and it is quite tolerant to the noise of the measurement data.